Quantitative Aptitude PYQs

Common Calculation –

According the question,

[ 8% + 12% + (2P + 5) % + P% + 15 %] = 100%

So, 2P + 5 + P = 100 – 15 – 12 – 8 = 65

Or, 3P = 60

Or, P = 60/3 = 20

So, Percentage distribution of number of items manufactured in factories A, B, C, D and E is 8%, 12%, [2 × 20 + 5] =45%, 20% and 15% respectively.

So, Item manufactured in factory A is 1200 × 8 /100 = 96

Similarly, we can calculate the number of items manufactured by others factory also, which is given in the table.

 

Calculation

Initial items

A = 96

D = 240

Transfer from D to A

25% of D = 25% of 240 = 60

New A = 96 + 60 = 156

Premium items in A = [20 + 5] % = 25% of 156 = 39 = P + 19

Common Calculation –

According the question,

[ 8% + 12% + (2P + 5) % + P% + 15 %] = 100%

So, 2P + 5 + P = 100 – 15 – 12 – 8 = 65

Or, 3P = 60

Or, P = 60/3 = 20

So, Percentage distribution of number of items manufactured in factories A, B, C, D and E is 8%, 12%, [2 × 20 + 5] =45%, 20% and 15% respectively.

So, Item manufactured in factory A is 1200 × 8 /100 = 96

Similarly, we can calculate the number of items manufactured by others factory also, which is given in the table.

 

Calculation

Factory C

Items = 540

Defect = 20% → 0.20 × 540 = 108

Non-defective = 432

Profit = 432 × 8 =  3456

Factory D

Items = 240

Defect = 12.5% → [1/8] × 240 = 30

Non-defective = 210

Profit = 210 × 20 =  4200

Factory E

Items = 180

Defect = 20% → [1/5] × 180 = 36

Non-defective = 180 – 36 = 144

Profit = 144 × 25 =  3600

Total profit = 3456 + 4200 + 3600 =11256

Common Calculation –

According the question,

[ 8% + 12% + (2P + 5) % + P% + 15 %] = 100%

So, 2P + 5 + P = 100 – 15 – 12 – 8 = 65

Or, 3P = 60

Or, P = 60/3 = 20

So, Percentage distribution of number of items manufactured in factories A, B, C, D and E is 8%, 12%, [2 × 20 + 5] =45%, 20% and 15% respectively.

So, Item manufactured in factory A is 1200 × 8 /100 = 96

Similarly, we can calculate the number of items manufactured by others factory also, which is given in the table.

 

Calculation

10% of C = 10% of 540 = 54

11.11% of E = (1/9) × 180 = 20

Total defective = 54 + 20 = 74 items

I. 6x² – 72x + 216 = 0

⇒ 6x² – 36x – 36x + 216 = 0

⇒ 6x(x – 6) – 36(x – 6) = 0

⇒ (x – 6)(6x – 36) = 0

⇒ x = 6

II. y² – 18y + 81 = 0

⇒ y² – 9y – 9y + 81 = 0

⇒ y(y – 9) – 9(y – 9) = 0

⇒ (y – 9)(y – 9) = 0

⇒ y = 9

∴ x < y.

Calculation:

I. 3x2 + 16x + 13 = 0

⇒ 3x2 + 3x + 13x + 13 = 0

⇒ 3x(x +1) + 13(x +1) = 0

⇒ x = - 13/3 or x = - 1

II. y2 + 9y – 36 = 0

⇒ y2 + 12y – 3y – 36 = 0

⇒ y(y + 12) – 3(y + 12) = 0

⇒ y = - 12 or y = 3

Comparison between x and y (via Tabulation):

∴ Relation between x and y can't be established

Given:

I. x² – 14x + 33 = 0

II. y² – 20y + 99 = 0

Calculation:

I. x² – 14x + 33 = 0

⇒ x² – 11x – 3x + 33 = 0

⇒ x(x – 11) – 3(x – 11) = 0

⇒ (x – 11)(x – 3) = 0

Then, x = 11 or x = 3

Now,

II. y² – 20y + 99 = 0

⇒ y² – 11y – 9y + 99 = 0

⇒ y(y – 11) – 9(y – 11) = 0

⇒ (y – 11)(y – 9) = 0

Then, y = 11 or y = 9

Now,

Comparison between x and y (via Tabulation):

∴ We can clearly see that the relationship cannot be established

Shortcut Trick

Initial CP for Suman = Rs. 100.

SP of Suman (to Rachna) = 100 × 1.10 = Rs. 110. (Profit = Rs. 10)

SP of Rachna (to Deepti) = 110 × 1.20 = Rs. 132.

SP of Deepti (to Suman) = 132 × (1 − 4/11) = 132 × 7/11 = Rs. 84. (Since 36.36% = 4/11)

Suman sold for Rs. 110 and bought back for Rs. 84, saving Rs. 26. ∴ The correct answer is Rs. 26.

Alternate Method

Given: Initial CP = Rs. 100, Profit₁ = 10%, Profit₂ = 20%, Loss₃ = 36.36%.

Formulas: Profit = SP − CP | SP = CP × (100 + P%)/100 | 36.36% = 4/11.

⇒ Profit 1 (Suman to Rachna): 10% of 100 = Rs. 10.

⇒ SP for Rachna = 100 + 10 = Rs. 110.

⇒ SP for Deepti = 110 + 20% of 110 = 110 + 22 = Rs. 132.

⇒ Loss for Deepti = 36.36% of 132 = (4/11) × 132 = 4 × 12 = Rs. 48.

⇒ Price at which Suman buys back = 132 − 48 = Rs. 84.

⇒ Total Profit of Suman = (Initial SP − Buyback Price) + Profit 1 = (110 − 84) + 0 = Rs. 26. (Alternative view: Suman started with 100, ended with the earpiece + Rs. 26 cash; since earpiece value is relative, we consider the cash differential from the transaction cycles).

∴ The correct answer is Rs. 26.

Additional Information

Percentage to Fraction Conversion

It is useful to remember that 9.09% = 1/11, hence 36.36% = 4/11. This simplifies calculations involving decimals.

Net Profit in Buyback

When a person sells an item and buys it back later, the net profit is the difference between the selling price and the re-acquisition price plus any profit made in the first sale.

Shortcut Trick

Total age 19 years ago = 86 − (19 × 2) = 48 years.

Ratio of Father : Son (19 years ago) = 5 :

1. Total units = 6 → 48 years ⇒ 1 unit = 8 years.

Son's age 19 years ago = 8 years ⇒ Present age = 8 + 19 = 27 years.

Wife's age = 27 − 6 = 21 years.

Ratio (Son : Wife) = 27 : 21 = 9 : 7.

∴ The correct answer is 9 : 7.

Alternate Method

Let the age of the son 19 years ago be x and the father's age be 5x.

⇒ Present age of son = x + 19

⇒ Present age of father = 5x + 19

⇒ (x + 19) + (5x + 19) = 86

⇒ 6x + 38 = 86

⇒ 6x = 48 ⇒ x = 8

⇒ Present age of Son = 8 + 19 = 27 years

⇒ Age of Wife = 27 − 6 = 21 years

⇒ Required Ratio = 27 : 21 = 9 : 7

∴ The correct answer is 9 : 7.

Additional Information

Age Sum Property

If the sum of ages of 'n' persons is S, then 't' years ago the sum was S − (n × t).

Ratio & Proportion

Ratio is the simplest form of comparison between two quantities of the same unit. Always simplify ratios by dividing by the HCF.

Constant Age Difference

The difference between the ages of two individuals remains constant regardless of the number of years passed.

Shortcut Trick

Sphere Surface Area 4πr² = 2464 ⇒ r² = 196 ⇒ r = 14 m ⇒ Diameter = 28 m.

Cone Height = 28 − 4 = 24 m; Radius = 7 m ⇒ Slant height (l) = √(24² + 7²) = 25 m.

CSA of Cone = πrl = (22/7) × 7 × 25 = 550 m².

Total Cost = 550 × 12 = Rs. 6600. ∴ The correct answer is Rs. 6600.

Alternate Method

Given: Surface Area of Sphere = 2464 m², Cone Radius (r_c) = 7 m, Cone Height (h_c) = Sphere Diameter − 4.

Formula Used: Surface Area of Sphere = 4πr²; Curved Surface Area (CSA) of Cone = πrl; Slant height l = √(r² + h²).

Step 1: Find Sphere Diameter

⇒ 4 × (22/7) × r² = 2464

⇒ r² = (2464 × 7) ÷ 88 = 28 × 7 = 196

⇒ Radius of sphere (r) = 14 m ∴ Diameter (D) = 28 m.

Step 2: Find Cone Dimensions

⇒ Height of cone (h_c) = 28 − 4 = 24 m.

⇒ Slant height (l) = √(7² + 24²) = √(49 + 576) = √625 = 25 m.

Step 3: Calculate Cost

⇒ CSA of cone = (22/7) × 7 × 25 = 550 m².

⇒ Cost of painting = 550 × 12 = Rs. 6600. ∴ The correct answer is Rs. 6600.

Additional Information

Volume of Sphere and Cone

Volume of sphere = (4/3)πr³ and Volume of right circular cone = (1/3)πr²h.

Total Surface Area of Cone

TSA of a cone includes the base area: TSA = πrl + πr² = πr(l + r).

Pythagorean Triplets

Frequent triplets like (7, 24, 25) help in finding the slant height (l) quickly without square root calculations.

Shortcut Trick

Since the Principal (P) and Time (T) are same, the difference in Amount is equal to the difference in Simple Interest.

Difference in Rate % for 2 years = (9% − 6%) × 2 = 6%

According to the question, 6% of P = ₹2166

P = (2166 ÷ 6) × 100 = 361 × 100 = ₹36100

∴ The correct answer is ₹36100.

Alternate Method

Given: Principal = ₹P, Time = 2 years, Rate_Amit = 9%, Rate_Rahul = 6%, Difference in Amount = ₹2166.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100; Amount = P + SI

⇒ Amount_Amit = P + (P × 9 × 2) ÷ 100 = P + 0.18P = 1.18P

⇒ Amount_Rahul = P + (P × 6 × 2) ÷ 100 = P + 0.12P = 1.12P

⇒ Difference = 1.18P − 1.12P = 0.06P

⇒ 0.06P = 2166

⇒ P = 2166 ÷ 0.06

⇒ P = 36100

∴ The correct answer is ₹36100.

Additional Information

Simple Interest Properties

Simple Interest is calculated only on the Principal amount. It remains constant for every year if the rate of interest is unchanged.

Difference between SI and CI

For the first year, Simple Interest and Compound Interest are the same. For 2 years, the difference is P(R/100)².

Effective Rate of Interest

In SI, the effective rate for 'T' years is simply (R × T)%. This helps in direct calculation of Interest or Amount.

Shortcut Trick

Initial average = 38, New average = 41.76, Increase = 3.76

Tournament average = 548 ÷ 7 ≈ 78.28

Using Alligation: (Initial matches) : (Tournament matches) = (78.28 − 41.76) : (41.76 − 38) = 36.52 : 3.76

Ratio = 3652 : 376 = 9.71 : 1 → Initial matches = 7 × 9.71 ≈ 68

Total matches = 68 + 7 = 75

∴ The correct answer is 75 matches.

Alternate Method

Let n be the number of matches before the tournament.

⇒ Total runs before = 38 × n

⇒ Total runs after = 38n + 548

⇒ Total matches played = n + 7

⇒ New average = (38n + 548) ÷ (n + 7) = 41.76

⇒ 38n + 548 = 41.76n + 292.32

⇒ 41.76n − 38n = 548 − 292.32

⇒ 3.76n = 255.68

⇒ n = 255.68 ÷ 3.76 = 68

⇒ Total matches = 68 + 7 = 75

∴ The correct answer is 75 matches.

Additional Information

Batting Average Formula

Batting Average = (Total runs scored) ÷ (Total number of times the batsman got out/Total innings played).

Net Deviation Method

Total Change = (New Count × New Avg) − (Old Count × Old Avg). This is useful for finding the value of new entries.

Weighted Average

Avg_combined = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where n is the quantity and A is the average.

Shortcut Trick

Equating Distance formula: D = [S₁ × S₂ / (S₁ − S₂)] × ΔT

[V × (V − 6) / 6] × (8 / 60) = [V × (V + 4) / 4] × (4.5 / 60)

⇒ (V − 6) / 6 × 8 = (V + 4) / 4 × 4.5 ⇒ 4(V − 6) / 3 = 1.125(V + 4)

⇒ V = 60 km/hr. Distance = [60 × 54 / 6] × (8 / 60) = 72 km.

∴ The correct answer is 72 km.

Alternate Method

Given: Case 1 speed = V − 6, Time = T + 8/60. Case 2 speed = V + 4, Time = T − 4.5/60.

Formula Used: Distance (D) = S₁ × S₂ × (Diff in Time) / (Diff in Speed)

⇒ D = [V(V − 6) / 6] × (8 / 60) --- (i)

⇒ D = [V(V + 4) / 4] × (4.5 / 60) --- (ii)

⇒ [V(V − 6) / 6] × 8 = [V(V + 4) / 4] × 4.5

⇒ 4 × (V − 6) / 3 = 1.125 × (V + 4) ⇒ 1.333(V − 6) = 1.125V + 4.5

⇒ 0.2083V = 12.5 ⇒ V = 60 km/hr

⇒ D = [60 × (60 − 6) / 6] × (8 / 60) = 540 × 8 / 60 = 72 km

∴ The correct answer is 72 km.

Additional Information

Constant Distance Formula

When a person travels at two different speeds S₁ and S₂ and the difference in time is ΔT, Distance D = (S₁ × S₂ / |S₁ − S₂|) × ΔT.

Average Speed

If the distance is constant, Average Speed = 2S₁S₂ / (S₁ + S₂). If time is constant, Average Speed = (S₁ + S₂) / 2.

Relative Speed

For two objects moving in the same direction, Relative Speed = |S₁ − S₂|. In opposite directions, Relative Speed = S₁ + S₂.

Common Calculation

Total number of employees in company A is 180.

Number of Graduate employees in Company A is 180 × 40/100 = 72

Number of Post graduate employees in company A is 180 – 72 = 108

Same way we can calculate other companies’ data, which is given in table.

 

Calculation

In Company B:

75% of graduates are males → 75% of 132 = 99

75% of postgraduates are females

→ So, males = 25% of 88 = 22

In Company C:

60% of graduates are females → 57.12% of 168 = 168 × [4/7]= 96

→ Male graduates = 168 – 96 = 72

50% of postgraduates are males → 50% of 72 = 36

Total male employees in B = 99 (graduates) + 22 (postgraduates) = 121

Total male employees in C = 72 (graduates) + 36 = 108

Final Answer: Total males in B + C = 121 + 108 = 229

Common Calculation

Total number of employees in company A is 180.

Number of Graduate employees in Company A is 180 × 40/100 = 72

Number of Post graduate employees in company A is 180 – 72 = 108

Same way we can calculate other companies’ data, which is given in table.

 

Calculation

Total postgraduate employees in E = 30

20% of 30 = (20/100) × 30 = 6